Analysis and estimation of error constants for P0and P 1 interpolations over triangular finite elements

Xuefeng Liu*, Fumio Kikuchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. For the piecewise linear one, we mainly analyze the conforming case, but the present results also appear to be available for the non-conforming case. We obtain explicit relations for the upper bounds of the constants, and analyze dependence of such constants on the geometric parameters of triangles. In particular, we explicitly determine some special constants including the BabuškaAziz constant, which plays an essential role in the interpolation error estimation of the linear triangular finite element. The obtained results are expected to be widely used for a priori and a posteriori error estimations in adaptive computation and numerical verification of numerical solutions based on the triangular finite elements. We also give some numerical results for the error constants and for a posteriori estimates of some eigenvalues related to the error constants.

Original languageEnglish
Pages (from-to)27-78
Number of pages52
JournalJournal of Mathematical Sciences
Issue number1
Publication statusPublished - 2010


  • Error estimates
  • FEM
  • Interpolation error constants
  • Triangular finite elements

ASJC Scopus subject areas

  • Mathematics(all)


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